(Phys.org)—Two teams of researchers working independently of one another have found ways to test aspects of the Tomonaga–Luttinger theory that describes interacting quantum particles in 1-D ensembles in a Tomonaga–Luttinger liquid (TLL). The first team, with members from China, Germany and Australia demonstrated TLL behavior with cold atoms in a 1-D array. The second team, with members from Australia, Germany and Russia, tested TLL predictions using a 1-D array of Josephson junctions to look at the impact of disorder in TLL physics. Both teams have published details of their work in Physical Review Letters.